/*
* Copyright (c) 1983 Regents of the University of California.
* All rights reserved. The Berkeley software License Agreement
* specifies the terms and conditions for redistribution.
*/
#if defined(LIBC_SCCS) && !defined(lint)
static char sccsid[] = "@(#)random.c 5.2 (Berkeley) 3/9/86";
#endif LIBC_SCCS and not lint
#include
/*
* random.c:
* An improved random number generation package. In addition to the standard
* rand()/srand() like interface, this package also has a special state info
* interface. The initstate() routine is called with a seed, an array of
* bytes, and a count of how many bytes are being passed in; this array is then
* initialized to contain information for random number generation with that
* much state information. Good sizes for the amount of state information are
* 32, 64, 128, and 256 bytes. The state can be switched by calling the
* setstate() routine with the same array as was initiallized with initstate().
* By default, the package runs with 128 bytes of state information and
* generates far better random numbers than a linear congruential generator.
* If the amount of state information is less than 32 bytes, a simple linear
* congruential R.N.G. is used.
* Internally, the state information is treated as an array of longs; the
* zeroeth element of the array is the type of R.N.G. being used (small
* integer); the remainder of the array is the state information for the
* R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
* state information, which will allow a degree seven polynomial. (Note: the
* zeroeth word of state information also has some other information stored
* in it -- see setstate() for details).
* The random number generation technique is a linear feedback shift register
* approach, employing trinomials (since there are fewer terms to sum up that
* way). In this approach, the least significant bit of all the numbers in
* the state table will act as a linear feedback shift register, and will have
* period 2^deg - 1 (where deg is the degree of the polynomial being used,
* assuming that the polynomial is irreducible and primitive). The higher
* order bits will have longer periods, since their values are also influenced
* by pseudo-random carries out of the lower bits. The total period of the
* generator is approximately deg*(2**deg - 1); thus doubling the amount of
* state information has a vast influence on the period of the generator.
* Note: the deg*(2**deg - 1) is an approximation only good for large deg,
* when the period of the shift register is the dominant factor. With deg
* equal to seven, the period is actually much longer than the 7*(2**7 - 1)
* predicted by this formula.
*/
/*
* For each of the currently supported random number generators, we have a
* break value on the amount of state information (you need at least this
* many bytes of state info to support this random number generator), a degree
* for the polynomial (actually a trinomial) that the R.N.G. is based on, and
* the separation between the two lower order coefficients of the trinomial.
*/
#define TYPE_0 0 /* linear congruential */
#define BREAK_0 8
#define DEG_0 0
#define SEP_0 0
#define TYPE_1 1 /* x**7 + x**3 + 1 */
#define BREAK_1 32
#define DEG_1 7
#define SEP_1 3
#define TYPE_2 2 /* x**15 + x + 1 */
#define BREAK_2 64
#define DEG_2 15
#define SEP_2 1
#define TYPE_3 3 /* x**31 + x**3 + 1 */
#define BREAK_3 128
#define DEG_3 31
#define SEP_3 3
#define TYPE_4 4 /* x**63 + x + 1 */
#define BREAK_4 256
#define DEG_4 63
#define SEP_4 1
/*
* Array versions of the above information to make code run faster -- relies
* on fact that TYPE_i == i.
*/
#define MAX_TYPES 5 /* max number of types above */
static int degrees[ MAX_TYPES ] = { DEG_0, DEG_1, DEG_2,
DEG_3, DEG_4 };
static int seps[ MAX_TYPES ] = { SEP_0, SEP_1, SEP_2,
SEP_3, SEP_4 };
/*
* Initially, everything is set up as if from :
* initstate( 1, &randtbl, 128 );
* Note that this initialization takes advantage of the fact that srandom()
* advances the front and rear pointers 10*rand_deg times, and hence the
* rear pointer which starts at 0 will also end up at zero; thus the zeroeth
* element of the state information, which contains info about the current
* position of the rear pointer is just
* MAX_TYPES*(rptr - state) + TYPE_3 == TYPE_3.
*/
static long randtbl[ DEG_3 + 1 ] = { TYPE_3,
0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342,
0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb,
0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86,
0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7,
0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b,
0xf5ad9d0e, 0x8999220b, 0x27fb47b9 };
/*
* fptr and rptr are two pointers into the state info, a front and a rear
* pointer. These two pointers are always rand_sep places aparts, as they cycle
* cyclically through the state information. (Yes, this does mean we could get
* away with just one pointer, but the code for random() is more efficient this
* way). The pointers are left positioned as they would be from the call
* initstate( 1, randtbl, 128 )
* (The position of the rear pointer, rptr, is really 0 (as explained above
* in the initialization of randtbl) because the state table pointer is set
* to point to randtbl[1] (as explained below).
*/
static long *fptr = &randtbl[ SEP_3 + 1 ];
static long *rptr = &randtbl[ 1 ];
/*
* The following things are the pointer to the state information table,
* the type of the current generator, the degree of the current polynomial
* being used, and the separation between the two pointers.
* Note that for efficiency of random(), we remember the first location of
* the state information, not the zeroeth. Hence it is valid to access
* state[-1], which is used to store the type of the R.N.G.
* Also, we remember the last location, since this is more efficient than
* indexing every time to find the address of the last element to see if
* the front and rear pointers have wrapped.
*/
static long *state = &randtbl[ 1 ];
static int rand_type = TYPE_3;
static int rand_deg = DEG_3;
static int rand_sep = SEP_3;
static long *end_ptr = &randtbl[ DEG_3 + 1 ];
/*
* srandom:
* Initialize the random number generator based on the given seed. If the
* type is the trivial no-state-information type, just remember the seed.
* Otherwise, initializes state[] based on the given "seed" via a linear
* congruential generator. Then, the pointers are set to known locations
* that are exactly rand_sep places apart. Lastly, it cycles the state
* information a given number of times to get rid of any initial dependencies
* introduced by the L.C.R.N.G.
* Note that the initialization of randtbl[] for default usage relies on
* values produced by this routine.
*/
srandom( x )
unsigned x;
{
register int i, j;
if( rand_type == TYPE_0 ) {
state[ 0 ] = x;
}
else {
j = 1;
state[ 0 ] = x;
for( i = 1; i < rand_deg; i++ ) {
state[i] = 1103515245*state[i - 1] + 12345;
}
fptr = &state[ rand_sep ];
rptr = &state[ 0 ];
for( i = 0; i < 10*rand_deg; i++ ) random();
}
}
/*
* initstate:
* Initialize the state information in the given array of n bytes for
* future random number generation. Based on the number of bytes we
* are given, and the break values for the different R.N.G.'s, we choose
* the best (largest) one we can and set things up for it. srandom() is
* then called to initialize the state information.
* Note that on return from srandom(), we set state[-1] to be the type
* multiplexed with the current value of the rear pointer; this is so
* successive calls to initstate() won't lose this information and will
* be able to restart with setstate().
* Note: the first thing we do is save the current state, if any, just like
* setstate() so that it doesn't matter when initstate is called.
* Returns a pointer to the old state.
*/
char *
initstate( seed, arg_state, n )
unsigned seed; /* seed for R. N. G. */
char *arg_state; /* pointer to state array */
int n; /* # bytes of state info */
{
register char *ostate = (char *)( &state[ -1 ] );
if( rand_type == TYPE_0 ) state[ -1 ] = rand_type;
else state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
if( n < BREAK_1 ) {
if( n < BREAK_0 ) {
fprintf( stderr, "initstate: not enough state (%d bytes) with which to do jack; ignored.\n" );
return;
}
rand_type = TYPE_0;
rand_deg = DEG_0;
rand_sep = SEP_0;
}
else {
if( n < BREAK_2 ) {
rand_type = TYPE_1;
rand_deg = DEG_1;
rand_sep = SEP_1;
}
else {
if( n < BREAK_3 ) {
rand_type = TYPE_2;
rand_deg = DEG_2;
rand_sep = SEP_2;
}
else {
if( n < BREAK_4 ) {
rand_type = TYPE_3;
rand_deg = DEG_3;
rand_sep = SEP_3;
}
else {
rand_type = TYPE_4;
rand_deg = DEG_4;
rand_sep = SEP_4;
}
}
}
}
state = &( ( (long *)arg_state )[1] ); /* first location */
end_ptr = &state[ rand_deg ]; /* must set end_ptr before srandom */
srandom( seed );
if( rand_type == TYPE_0 ) state[ -1 ] = rand_type;
else state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
return( ostate );
}
/*
* setstate:
* Restore the state from the given state array.
* Note: it is important that we also remember the locations of the pointers
* in the current state information, and restore the locations of the pointers
* from the old state information. This is done by multiplexing the pointer
* location into the zeroeth word of the state information.
* Note that due to the order in which things are done, it is OK to call
* setstate() with the same state as the current state.
* Returns a pointer to the old state information.
*/
char *
setstate( arg_state )
char *arg_state;
{
register long *new_state = (long *)arg_state;
register int type = new_state[0]%MAX_TYPES;
register int rear = new_state[0]/MAX_TYPES;
char *ostate = (char *)( &state[ -1 ] );
if( rand_type == TYPE_0 ) state[ -1 ] = rand_type;
else state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
switch( type ) {
case TYPE_0:
case TYPE_1:
case TYPE_2:
case TYPE_3:
case TYPE_4:
rand_type = type;
rand_deg = degrees[ type ];
rand_sep = seps[ type ];
break;
default:
fprintf( stderr, "setstate: state info has been munged; not changed.\n" );
}
state = &new_state[ 1 ];
if( rand_type != TYPE_0 ) {
rptr = &state[ rear ];
fptr = &state[ (rear + rand_sep)%rand_deg ];
}
end_ptr = &state[ rand_deg ]; /* set end_ptr too */
return( ostate );
}
/*
* random:
* If we are using the trivial TYPE_0 R.N.G., just do the old linear
* congruential bit. Otherwise, we do our fancy trinomial stuff, which is the
* same in all ther other cases due to all the global variables that have been
* set up. The basic operation is to add the number at the rear pointer into
* the one at the front pointer. Then both pointers are advanced to the next
* location cyclically in the table. The value returned is the sum generated,
* reduced to 31 bits by throwing away the "least random" low bit.
* Note: the code takes advantage of the fact that both the front and
* rear pointers can't wrap on the same call by not testing the rear
* pointer if the front one has wrapped.
* Returns a 31-bit random number.
*/
long
random()
{
long i;
if( rand_type == TYPE_0 ) {
i = state[0] = ( state[0]*1103515245 + 12345 )&0x7fffffff;
}
else {
*fptr += *rptr;
i = (*fptr >> 1)&0x7fffffff; /* chucking least random bit */
if( ++fptr >= end_ptr ) {
fptr = state;
++rptr;
}
else {
if( ++rptr >= end_ptr ) rptr = state;
}
}
return( i );
}